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Chapter 5, Problem 2CRE

Ohio Pick 4 In Ohio’s Pick 4 game, you pay $1 to select a sequence of four digits, such as 7709. If you buy only one ticket and win, your prize is $5000 and your net gain is $4999.

  1. a. If you buy one ticket, what is the probability of winning?
  2. b. Construct a table describing the probability distribution corresponding to the purchase of one Pick 4 ticket.
  3. c. If you play this game once every day, find the mean number of wins in years with exactly 365 days.
  4. d. If you play this game once every day, find the probability of winning exactly once in 365 days.
  5. e. Find the expected value for the purchase of one ticket.
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13. Let (, F, P) be a probability space and X a function from 2 to R. Explain when X is a random variable.
24. A factory produces items from two machines: Machine A and Machine B. Machine A produces 60% of the total items, while Machine B produces 40%. The probability that an item produced by Machine A is defective is P(DIA)=0.03. The probability that an item produced by Machine B is defective is P(D|B)=0.05. (a) What is the probability that a randomly selected product be defective, P(D)? (b) If a randomly selected item from the production line is defective, calculate the probability that it was produced by Machine A, P(A|D).

Chapter 5 Solutions

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